Macroscopic three-loop amplitudes and the fusion rules from the two-matrix model

From the computation of three-point singlet correlators in the two-matrix model, we obtain an explicit expression for the macroscopic three-loop amplitudes having boundary lengths l i (i = 1, …, 3)in the case of the unitary series (p,q) = (m + 1,m) coupled to two-dimensional gravity. The sum appearing in this expression is found to conform to the structure of the CFT fusion rules while the summand factorizes through a product of three modified Bessel functions. We briefly discuss a possible generalization of these reatures to macroscopic n-loop amplitudes.